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Surveying‐I (130601)CHAPTER ‐44CURVES20 September 2013
Question asked in GTU‐TheoryGTU Theory1)) Describeesc be tthee pprocedureocedu e oof settsettingg out oof ssimplepecircular curve by (i) Perpendicular offset fromtangent, and (ii) Rankine’s method of tangentialangle.l Dec‐20092) Why transition curves are introduced onh i t l curves off highwayshorizontalhi hor railways?il? Dec‐D20093) Describe the method of setting a circular curveby the method of offsets from the long chord.Dec‐201020 September 2013
Question asked in GTU‐TheoryGTU Theory4)) Discuss the method of settingg out a circular curvewith two theodolite. What are its advantagesand disadvantages over Rankine’s method Dec‐20105) What are the elements of simple circular curve?Define with figure and give their relationship.March‐20106) Why are curves provided? State various types ofcurves with sketchsketch.7) Draw the neat sketch of simple circular curveshowingg various elements of it. Dec‐201120 September 2013
Question asked in GTU‐TheoryGTU Theory8) Enumerate the parts of a compound curveand describe the relationship between themJan 2013.Jan‐20139) What is vertical curve? Explain different typesof vertical curves.curves Jan‐2013.Jan 201310) Explain following terms (i) Compound curve(ii) PointP i off intersectionii (iii) TangentTDiDistance(iv) Mid Ordinate May‐2012.20 September 2013
Lecture outline Introduction Theory and setting out methods of simplecircular curve Elements of compound and Reverse curve. Transition curve Types of Transition curve CombinedC bi d curve Types of vertical curve.20 September 2013
What is curve? Why Curve? Use off CCurve.20 September 2013
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Components of Highway DesignHorizontal AlignmentPlan ViewV ti l AlignmentVerticalAlitProfile View20 September 2013
Horizontal AlignmentToday’sTd ’ Class:Cl Components of the horizontal alignment Properties of a simple circular curve20 September 2013
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Types of Curve Curves Horizontal CurveCircular CurveTransition Curve1) Simple curve1) Cubic parabola2) Compound Curve 2 ) Spiral Curve3) Reverse Curve3) Lemniscate20 September 2013Vertical CurveSummit CurveValley Curve
Types of Circular Curve20 September 2013
Types of Circular Curve20 September 2013
Types of Circular Curve20 September 2013
Definition and Notation of Simple Curve20 September 2013
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Definition and Notation of Simple Curve 1) Back tangent or First Tangent ‐ AT₁– Pervious to the curve2) Forwardd Tangent or Secondd tangent‐ B T₂‐ Following the curve.3) Point of Intersection ( P.I.) or Vertex. (v)If the tangents AT₁ and BT₂ .are produced theywillill meett ini a pointi t calledll d theth pointi t offintersection4)Point of curve ( P.C.)P C ) –BeginningBeginning Point T₁T of acurve. Alignment changes from a tangent tocurve.20 September 2013
Definition and Notation of Simple Curve 5)) Point off Tangency ‐ PT– End point of curve ( T₂ ) is called.6)) Intersection Angleg (Ø )‐ The Angle AVB between tangent AV and tangent VB iscalled.7) Deflection Angle ( )The angle at P.I. between tangent AV and VB is called.8)Tangent Distance –It is the distance between P.C. and P.I.9) External Distance – CIThe distance from the mid point of the curve to P.I.It is also called the apex distance.10) Length of curve – lI isIti theh totall lengthlh off curve fromfP C to P.TP.C.PT.20 September 2013
Definition and Notation of Simple Curve11) Long Chord– It is the chord joining P.C. to P.T., T₁ T₂ is a long chord.12) Normal Chord:A chord between two successive regular station on a curve iscalled normal chord. Normally , the length of normal chord is 1chain ( 2o mt).13) Sub chordThe chord shorter than normal chord ( shorter than 20 mt) iscalled sub chord)14) Versed sine – Distance CDThe distance between mid point of long chord ( D ) and the apexpoint C, is called versed sine. It is also called mid‐ ordinate ( M).15) Right hand curve:If the curve deflects to the right of the direction of the progressof survey.16) Left hand curveIf theth curve deflectsd fl t tot theth leftl ft off theth directiondi ti off theth progressof survey.20 September 2013
Designation of curveThe sharpness of the curve is designated by twoways.( 1 ) By radius ( R)( 2) ByB DegreeDoff CurvatureCt(D)( 1 ) By radius ( R)Curve is known by the length of its radius‐radius R20 September 2013
Designation of curve( 2) By Degree of Curvature ( D )Chord DefinitionArc DefinitionThe Angle subtended atthe centre of curve by achordh d off 30 or 20 mt. isicalleddegreeofcurvature.The Angle subtended atthe centre of curve by an30 or 20 mt.arc oflength is called degree ofcurve.If an angle subtended atthe centre of curve by achord of 20 mt is 5 , the20 September 2013curve is called 5 curveUsed in America, canada,India etc.etc
Relation between Radius and degree of curve.( ) By(a)B chordh dddefinitionfi itiThe angle subtended at the centre of curveby a chord of 20 mt. is called degree of curve.R radius of curve.D degree of curve.PQ 20 mt. Lengthg of chord.From Triangle PCO20 September 2013
Relation between Radius and degree of curve.When D is small,20 September 2013may taken equal to
Relation between Radius and degree of curve.(b) By Arc Definition :The angle subtended at the centre of curve byan arc of 20 mt. length is called degree ofcurve.20 September 2013
Elements of Simple circular curve20 September 2013
Elements of simple circular curve20 September 2013
Elements of Simple circular curve T₁ P.C. Point of tangency Point of curve.T₂ P.T.P.T. Second point of tangency.V or I P.I. Point of intersection. DDeflectionfl ti angle.lØ Intersection angle.R Radius of curve.CD Mid ordinate (M)CD20 September 2013
Example 1 A circular curve has a radius of 150 mt and 60⁰deflection angle. What is its degree(i) By arcdefinition and 9ii) by chord definition. Solution:(i) By arc definition Assuming chord length 30mt20 September 2013
Elements of Simple circular curve 1) Length of curve ( l) * If curve is designatedgbyy Radius:l Length of arc T₁ C T₂ R* ‐ When is in Radian‐ When is in degree.* If curve is designated by degree: Length of arc 20 mt. Length of curve20 September 2013
Elements of Simple circular curve2) Tangent length ( T): VT₁VT and VTVT₂ are the tangents length Elementsof simple circular curve T VTVT₁ VT₂VT tangenttt llengthth From VT₁O20 September 2013
Elements of Simple circular curve3) Length of chord ( L ):Elements of simplecircular curve In the figure T₁ ,T₂ is a long chord. LengthL th off llong chordh d LL T₁T₂T T 2 * (T₁(T D).D) From triangle T₁DO,20 September 2013
Elements of Simple circular curve4) External Distance ( E ): or ApexdistanceElements of simple circular curve In the figure VC is an external distance. External distance E VC OV –OC Length of From triangle VT₁O.E OV‐OC ( OC R)20 September 2013
Elements of Simple circular curve 5) Mid ordinate ( M ): Distance – CDAlso known as versed sine of the curve.Mid ordinate M CD OC‐ODFrom T₁DO 20 September 2013M OC‐ OD
Setting out of single Circular curve First step‐ Locate tangent point ‐ By tape measurements.‐Intersection of both tangents point V‐ Pointof intersection.‐ Set theodolite at V and measure angle Ø‐Ø ( Measure by theodolite)‐ Calculate tangent length‐ Fix point T₁T₂20 September 2013
Setting out of single Circular curve Chainage of tangents: ‐ Point A is the starting point of chain line Chainage of point V, B, D are measured frompoint A.p ‐ Chainage of T₁ Chainage of V‐ T ( Tangent length) T ChainageT₂Chainage of TT₁ Length of curve (l)20 September 2013
Setting out of single Circular curve NormalNl chordh d andd SubS b chord:h d ‐For alignment pegs are driven. Theh distancedibbetweentwo pegs isi normallyll 20m20 Peg station are called main stations. The chord joining the tangents point T₁ and the firstmain peg station is called First sub chord. All theth chordh d joiningj i iadjacentdjt peg stationst tiarecalled full chord or normal chord. The length of normal chord is 20 mt.mt The point joining last main peg station and tangentT₂ is called last sub chord.chord20 September 2013
Methods of Setting out of single Circular curve Two Methods 1) Linear Methods 2) Angular Methods. 1) Linear Methods‐ (i)( ) By offsetsffor ordinatedfromftheh longlchord.h d(ii) By successive bisection of arcs or chords.(iii) By offsets from the tangents.(iv) By offsets from the chord producedproduced.20 September 2013
(i) By offsets or ordinate from the long chord.R Radius of curveO0 Mid ordinateOx Ordinate at distance xT1, T2 tangents pointL Length of long chord.20 September 2013
(ii) By successive bisection of arcs or chords. T1‐T2 T1T2 LT1‐C LT2‐C LC‐C1,, C‐C2 LC1‐T1, C2‐T2 L20 September 2013
(iii) By offsets from the tangents. Two typesRadial offsetPerpendicularpoffset20 September 2013
Angular Method Used when length of curve is large More accurate than the linear methods.methods Theodolite is used The angular methods are:1) Rankine method of tangential angles.OROne theodolite method2) Two theodolite method.20 September 2013
Obstacles in setting out simple curvesCase –I -When P.I. is inaccessibleCCase–IIII -WhenWhP.C.P C iis inaccessibleiiblCase –III -When P.T. is inaccessibleCase –IV - When both P.C. and P.T. isinaccessible. Case –V - When obstacles to chaining. 20 September 2013
TRANSITION CURVE20 September 2013
Requirement of transition curveTangential to straightM t circularMeeti l curve ttangentiallyti llAt origin curvature should zero.Curvature should same at junction of circularcurve. Rate of increase of curvature rate increase ofp elevation.super Length of transition curve full superelevation attainedattained. 20 September 2013
Purposepof transition curve Curvature is increase gradually. Medium for gradual introduction ofsuperelevation Provide Extra widening gradually Advantages Increase comfort to passenger on curve Reduce overturning Allow higher speed Less wear on gear, tyre20 September 2013
Types of transition curve Cubic parabola ‐ For railway Spiral or Clothoid‐ Ideal transition‐ Radius α Distance Lemniscates‐ Used for road20 September 2013
Vertical curve20 September 2013
Length of vertical curve Total change of grade Length of vertical curve �‐‐‐‐‐‐‐‐‐‐‐ Rate of change of grade g2 – g1 �‐ r g1, g2 Grades in % r Rate of change of grade20 September 2013
Define with figure and give their relationship. March‐2010 6) Why are curves provided? State various types of curves with sketch. 7) Draw the neat sketch of simple circular curve s
